EMSW21-RTG: Graduate Education in Geometry and Topology at the University of Chicago

摘要奖：DMS-0354270主要研究者：Kevin D. Corlette这个项目将支持芝加哥大学几何/拓扑组的活动，这些活动对研究生的培训有影响。 这个小组目前由六名高级教师，十三名初级教师和大约三十名研究生组成。 该小组成员的研究兴趣涵盖了几何和拓扑学的广泛主题，包括复微分几何，刚性和局部对称空间，遍历理论与离散群和数论的联系，几何群论，3-流形拓扑，Teichmuller理论，高维流形的几何拓扑，黎曼度量的模空间，复动力学，辛拓扑和同伦理论。 该小组的活动包括积极的研究研讨会在几何/拓扑和代数拓扑，severalstudent研讨会和一个访问者计划，所有这些都是直接相关的研究生教育。 这些活动，在该部门的研究生课程的总体结构相结合，为学生提供理想的条件，以获得接触到广泛的当前研究，同时追求自己的具体研究项目。几何和拓扑是数学的基本组成部分，这是目前正在经历快速发展，有许多新的想法和调查线正在追求。 这些发展中的许多是内部的主题，而其他人出现，至少部分，从接触领域，如物理学和计算机科学。 作为一名学生，在经历这种变化的领域中学习是特别令人兴奋的，但同时，在景观迅速变化的情况下，定位自己也是一个挑战。 该项目将提高芝加哥大学博士生在这些领域学习和研究的能力，从而有助于培养下一代几何和拓扑学研究人员。 除了为研究生的研究提供直接支持外，该项目还将为研究生提供支持，让他们前往参加会议，并将访问者带到大学进行研讨会和合作。 所有这些都是为了让研究生尽可能有效地接触研究的前沿。

AbstractAward: DMS-0354270Principal Investigator: Kevin D. CorletteThis project will support activities of the geometry/topologygroup at the University of Chicago which have an impact on thetraining of graduate students. This group currently consists ofsix senior faculty, thirteen junior faculty and about thirtygraduate students. The research interests of members of thegroup span a wide array of topics in geometry and topology,including complex differential geometry, rigidity and locallysymmetric spaces, connections of ergodic theory with discretegroups and number theory, geometric group theory, 3-manifoldtopology, Teichmuller theory, geometric topology ofhigh-dimensional manifolds, the moduli space of Riemannianmetrics, complex dynamics, symplectic topology and homotopytheory. The activities of the group include active researchseminars in geometry/topology and algebraic topology, severalstudent seminars and a visitors program, all of which aredirectly relevant to the education of graduate students. Theseactivities, in combination with the general structure of thegraduate program in the department, provide ideal conditions forstudents to gain exposure to a broad range of current researchwhile pursuing their own specific research projects.Geometry and topology are fundamental parts of mathematics whichare currently experiencing rapid development, with many new ideasand lines of investigation being pursued. Many of thesedevelopments are internal to the subject, while others arise, atleast in part, from contact with fields such as physics andcomputer science. It is particularly exciting to be a student ina field undergoing this kind of change, but it is at the sametime a challenge to orient oneself when the landscape is rapidlychanging. This project will enhance the ability of doctoralstudents at the University of Chicago to learn about and doresearch in these areas, thus helping to train the nextgeneration of researchers in geometry and topology. In additionto providing direct support for graduate students as they doresearch, the project will also provide support for graduatestudents to travel to conferences and the bring visitors to theUniversity for seminar talks and collaboration. All of this isintended to expose graduate students to the frontlines ofresearch as effectively as possible.